たところ

Expresses that an action has just been completed at the moment of speaking. It emphasizes the point in time immediately after the action finished.

Neutral in register and common in both conversation and writing, often with time words like 今, さっき or ちょうど. It stresses the precise moment right after completion, such as when explaining your current situation. Unlike たばかり, which can describe events felt to be recent even if days or months have passed, たところ refers only to the time immediately after an action.

• 〜たところだN3「〜たところだ」 corresponds only to the 'just did...' sense of this pattern, and in that sense the two are interchangeable; it has no 「たところ、…」 'did... and then discovered...' usage, and it cannot combine with time words from further back such as 「先月」.
• たばかりN4「たばかり」 also expresses 'just...', but it centers on the speaker's subjective feeling that not much time has passed, so it can be used with 「先月」 or 「去年」; it can also modify a noun, as in 「たばかりの＋noun」, and it has no result-expressing usage like 「たところ、…」.
• ているところN4「ているところ」 attaches to 「て形＋いる」 and indicates that the action is in progress and not yet finished, either at the moment of speaking or at some point in the past; 「たところだ」 indicates the action has just been completed, so the two cover different time stages and cannot be interchanged. 「たところ、…」 expresses a result and is unrelated to it.
• 〜るところだN3「〜るところだ」 attaches to the verb's 辞書形 and indicates the action is about to begin ('about to...'), while 「たところだ」 attaches to the た形 and indicates it has just been completed — the two mark exactly the moments just before and just after the action, so they cannot be interchanged. It has no counterpart to the 「たところ、…」 usage of discovering a result after doing something.
• たとたんN3「たとたん」 emphasizes that the second action appears almost the instant the first one occurs, and that the second action is usually an uncontrollable change; 「たところだ」 refers to having just finished at the moment of speaking, while 「たところ、…」 refers to a result discovered after doing something and does not require immediacy, so generally they cannot be interchanged.

〜たところだ is the same construction, and たばかり also means 'just did' but allows a longer, subjectively felt time span. ているところ marks an action in progress, 〜るところだ an action about to happen, and たとたん means 'the moment X happened, Y (unexpectedly) followed.'