No, its certainly not uniform.

In the US or British armies, especially beginning in 1944, if your unit is still in combat (which it most likely is) you absorbed replacements by a drip effect; manpower crises (especially with the British) meant that effective replacement systems went out the window for speed and rapidity. By 1944, the British were amalgamating divisions and disbanding the worse-hit regiments - this is what happens when an Island nation wages war for six years. In the US, replacements, especially to front line units, were shipped individually; a replacement could train with a group, but then be shipped off to a smattering of other units. When they arrived at the front, they were greeted by quite literally no familiar faces; the effectiveness (rather, the lack there of) is self-explanatory and for a US replacement, his first few weeks at the line were his most dangerous time - many inexperienced and unknown recruits were brought into the ranks, killed or wounded, and rotated out of the ranks before any veterans bothered to get to know them. It was a highly ineffective system born out of necessity, more so than poor direction, that was replaced by the Training Battalion system post-war.

There are minor exceptions to the rule for the US, however. Two separate Armored Infantry units; two battalions that remained stateside to absorb replacements, train them in batches, and ship them off to units (ironically, not always Armored Infantry battalions). Generally however, the trend of reinforcements follows the aforementioned pattern.

For the Germans, all divisions had an Ersatz battalion; a dedicated replacement battalion, that remained in barracks to absorb, train, and then ship off replacements to the parent division. The advantages of this on the psyche and morale of a recruit were phenomenal: they arrived with familiar faces whom they had been training and building a rapport with, and arrived with foreknowledge of their parent unit and perhaps even their immediate commander's name. Replacements as a concept however, become more laughable the closer you get to Summer 1944. As the manpower crisis evolved, and the Allied and Soviet lines advanced, it wouldn't be out of the question as an Ersatz member to find yourself training the hard way; by fighting. Many AA and NCO ersatz units were overrun and forced to fight in Lorraine and Metz, for example.

For the Soviets it was more often the case to create new formations rather than attempt to replenish those already in combat. Stavka reserves were created endlessly, ready to assimilate tired units or pass through them to continue the fight. With the very idea of Russia in mortal peril in 1941 and 1942, many divisions fought to utter exhaustion or the cessation of their existence, so determined was Soviet resistance and so immediate the threat. Replacements were difficult especially to obtain during those years as Luftwaffe interdiction was merciless; as I said - easier and safer to form new formations instead.