They depend on the unhairing method used. They are done in one bath. According to technologists this process is done properly if:
beside the removal of Ca⁺² ions from pelt it meets the following requirements:
1)the pH inside the collagen network is regulated and the bath is buffered
2)swelling is reduced to the expected degree
3)fibers are separated by washing out matrix.
4)products of protein degradation are removed from pelt.
Points 1 and 2 are chemical, points 3 is chemical and enzymatic, point 4 is enzymatic only.
Approximately 2/3 of the Ca(OH)₂ in the pelt after liming may be removed by washing. Further washing does not remove more. Higher temperature may help but pelt will be less plump then. Ca⁺²   may form the sulfate in tanning therefore should be removed.
Deliming should be carried gradually, slowly due to the pH inside the pelt. Buffered systems from slowly dissociating acids and appropriate salts are used.
Problems of removing iron ions (from blood or water) from the hide are combined with deliming and are removed by EDTA.
EDTA-Cr⁺³  complexes penetrate in pelt, react with Ca and Fe ions making Cr⁺³ ions free(tanning properties).
EDTA-Cr⁺³  stable < pH 4.5  at pH=7 half is set free
EDTA-Ca⁺²  stable < pH 9    at pH=7 half is set free
In this way, putting a limed pelt, rinsed with warm water in float pH 2.5 one has two effects, deliming and tanning. Tanning is low at start then due to changes in masking, it becomes faster when going deeper into the pelt (not used in industry).
Bating is done in the same operation.It means final removal of non-collagenous hide components, keratin, degradation products, globular proteins, elastin and cell structure residues. A condition of success is avoiding negative action of deliming on enzymes used for bating.

After liming, the lime or other alkali in the skin is no longer required, and in most cases it has detrimental effect on subsequent tannage. With chrome tanning it gives a hard green inflexible leather and prevents proper tannage, whilst with vegetable tanning it also slows down or reduces tannage and gives a dark color.
Washing: The easiest way of removing the lime is to put the skins into a paddle or drum and to run them, whilst a continuous flow of cold clean water is fed in. Washing readily removes undissolved lime from the surface, and some dissolved lime held between the fibres. Some of the lime or other alkali such as caustic soda, is chemically held by fibres (about 0.4 % on the weight of skin) and this is only very slowly removed by washing. The process becomess progressively slower and slower as the lime is removed. 
Dangers associated with prolonged washing: hard water may cause Lime Blast
(soluble Ca or Mg bicarbonates or carbonic acid react with lime to ppt CaCO₃).
Prolonged washing allows further alkali breakdown of the skin to occur, giving loose leather, particularly if the water is warm. Warm water (35 ⁰C) will reduce lime plumping of the fibre structure, thus allowing easier access of water to wash out interfibre protein and lime. Maximum permissible temperature is 38 ⁰C.
Chemical deliming: Speeds up washing process and avoids difficulties. The loose lime is removed by wasing, as above, the supply of water is turned off, and controlled amounts of acids or acid producing salts are added to the water. The acids neutralize the alkali. Too much acid damages the skin by causing violent swelling and solution of protein. As it is impossible to estimate accurately the amount of alkali in a pack of limed goods, it is usual to use either the weak organic acids- boric (or boracic), lactic,acetic acid- or acid salts such as sodium bisulphite, or salts of week alkalis such as ammonium chloride, ammonium sulphate. All of these give less danger of over-deliming with consequent acid swelling than the strong, cheap mineral acids, hydrochloric and sulphuric acid. The ammonium salts while reducing alkalinity, therefore reducing alkali swelling, are incapable of bringing the skin into acid condition.
Weak acids (and weak bases) and their salts give buffer systems. I it is required to adjust the pH of a skin to a certain figure it is practical to choose a weak acid(or base) with pK value near to the required pH.
Formic acid 3.7
Acetic acid 4.7
Boric acid 9.2
Ammonia 8.6
Some modern systems of deliming use non-swelling acids. These may be quite strong acids but due to the potential dipoles in their structure they do not swell the protein.
May contain phthallic acid types or complex meta phosphates.
Extent of deliming is estimated by making a clean cut in the skin and checking the pH.
Degree of deliming given depends on the process which is to follow. One of these the bating process is carried out at pH 8 and use of ammonium salts is particularly suitable.
Where this process is omitted it is still necessary to reduce the alkalinity for tannage.
In the case of many vegetable tannages for heavy leather, this is achieved by the acidity of the tan liquors themselves. For vegetable tannage, oil tannage or formaldehyde tannage of lighter leathers, such as sheep or goat, further deliming or acidification is given by drenching or souring process with weak organic acids. For the minneral tannages, such as chromium or alum, this process may also be used but it is much more common to use a pickling process employing mineral acids, such as sulphuric acid or hydrochloric acid, and salt. This can give a much more acid skin with a pH of 2-4, at which these tannages commonly start.
Delimed skins must be taken to the next process immediately, as the alkali has been removed and putrefying bacteria can cause a slimy feel and loose leather with damaged structure.

Additional removal of protein material loosened by liming is achieved by enzymatic digestion- the operation of bating.
Based on sterile enzymes (origins :pepsin and trypsin in dog dung and fowl droppings were used once upon a time; causing a soft smooth and silky grain) .
Two main types: 
pancreatic bates: digestive enzymes from pancreatic glands.
bacterial bates: digestive enzymes of bacteria.
They are prepared in sterile conditions, mixed with fine wood flour and ammonium salts(sulphate or chloride). Ammonium salts keep the pH at best level for the action of the enzyme.
Method:
The hides and skins are delimed to a pH of 8.0-8.5 and washed. This is the degree of alkalinity at which most enzymes show greatest digestive power. The goods are then usually treated in 300-500 % water at 37 ⁰C with a 1-2 % addition of the powdered enzyme mixture. It is important to maintain the pH and temperature accurately, as slight variations give great loss of bating power.
When slight flattening of the grain or increase in flexibility is required the time of bating is short (ie.1 hr).Longer bating times are necessary for extreme stretch and suppleness. The digestive action of bating is stopped by making conditions unsuitable for enzyme activity (ie. Cooling to 16 ⁰C, make more acid, or cstart tannage).
Care should be taken not to immerse skins directly from bating to cool water or remains of the erector pili muscles will contract giving “goose pimple” effect.
Enzyme is not used up by the process and old bate liquors can be as strong as fresh ones. There also is the probability of contamination or infection by other putrefying bacteria.
Most important points to control:
pH of the skin(alkalinity on the cross section of the skin), temperature and time.
If a good bating on the grain is desired to get a smooth, flat and scud-free surface but to bate the corium is undesired, the hide or skin is lightly delimed with ammonium salts to give surface pH 8.5 while the corium is still pH 11. With a short bating time one will get good bating on the grain and very little in the corium. With time the difference in pH will be uniform through the skin structure.
Other bating preparations are made where optimum pH for enzyme activity is different,(ie.acid bates)pH 4 or 5. They may give softer leather because at these pH the fibres are not swollen and allow easier access of enzyme and carrier to enter fibre structure. They are often useful for bating already pickled stock whan the acidity is neutralised with about 1 % sodium acetate to raise the pH to 4.7- 5.0, the goods rinsed to remove some salt and bated as specified.
Bate scudding: bated skins are scudded when it is essential to get very clean grain.The material squeezed out consist of hair roots,pigments, fat epidermis and unwanted protein.