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A.  I'm off now.  See you tomorrow.
B.  I'll be off now.  See you tomorrow.

1. Which of the above is naturally said when one is about to leave?  I usually hear it in the UK, but I don't clearly hear whether they've said "am off" or "will be off".
2. What is the difference in meaning between A and B?

Please advise.  Thank you.
Comments  
1. Both are valid, common alternatives.
2. There is no difference in meaning.
Thank you. That was helpful.
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There is a slight difference in context in the US

A. I'm off now. See you tomorrow. It's the end of a shift or work day. I'm finished and going home and tell my colleagues good-bye.

B. I'll be off now. See you tomorrow. It's the end of a meal, or having a fun with friends. I need to take my leave and go back to work, or go home.
Thank you for that additonal explanation.

Just for clarification, can I also say B in the context of your explanation in A that I'm finished with my work and leaving?
On the other hand, would you say that it would not be appropriate to say A in the context of your explanation in B because B is not work-related?
There's no rule about this. You can use either one and no one else will blink. I was giving you my experience on the situations when I hear each expression most often.
Students: We have free audio pronunciation exercises.
Thank you for that clarification. This is clear to me now. Emotion: smile
anonymousA. I'm off now. See you back work tomorrow.
B. I'll be off now. See you tomorrow.
1. Which of the above is naturally said when one is about to leave? I usually hear it in the UK, but I don't clearly hear whether they've said "am off" or "will be off".
2. What is the difference in meaning between A and B?
Please advise. Thank you.